{
  "id": 2590,
  "curve_key": "2695495608693409:-139698498155331274799473",
  "ainvs": [
    "1",
    "0",
    "0",
    "-56156158514446",
    "161688071888990580740"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.59107544508166,
  "faltings_height": 6.677152083851239,
  "conductor": "5064510990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "29",
    "173"
  ],
  "discriminant": "39920618726952768280799141699294488166400",
  "regulator": "13.6739416141697194816185461236738327122299",
  "points": [
    [
      "4137668",
      "411015866"
    ],
    [
      "4166396",
      "205639394"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=48; A=(3q-p)(p+q)^3=1186607, B=-(p+3q)(p-q)^3=52501295. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:11:19",
  "updated_at": "2026-09-26 20:11:19"
}